Course Description
This advanced course provides a detailed portfolio of techniques for performing model-based Bayesian statistics in (but not restricted to) experimental physics. It intertwines formal mathematics with computational methods to facilitate the implementation of statistical models tailored to a specific problem.
The course begins with basic concepts in inference and probability theory. Single- and multi-variate linear models are then discussed along with numerous real-life applications using the R programming language. Particular emphasis is placed on techniques for assessing model adequacy for a given dataset and for comparing models between them.
The course subsequently focuses on multilevel analyses to identify the global properties of a population of entities. It also highlights pitfalls in statistical modelling arising from the experimental setup, including issues related to sample completeness, biases and sensitivity.
Practical implementations of sampling techniques are presented, including Markov chain Monte-Carlo and nested sampling. Finally, the course introduces non-linear models as well as the implementation of Gaussian processes and machine learning approaches.
